Finite Group Databasebeta

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C₂³×#2436 #72324528

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

323573 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

(8,10)(15,16,19,18)(17,21,22,20);(8,10)(12,14)(15,16,19,18)(17,21,22,20);(3,4);(5,6);(12,14)(15,17,19,22)(16,20,18,21);(1,2)(3,4)(5,6);(7,8,9,10)(11,12,13,14)(15,18,19,16)(17,21,22,20)

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((8,10)(15,16,19,18)(17,21,22,20), (8,10)(12,14)(15,16,19,18)(17,21,22,20), (3,4), (5,6), (12,14)(15,17,19,22)(16,20,18,21), (1,2)(3,4)(5,6), (7,8,9,10)(11,12,13,14)(15,18,19,16)(17,21,22,20));